Sanger (submitted) argues for the interpretation of
neural activity in terms of external (sensory or motor)
conditional probability density functions (CPDFs) corresponding to their
generalized receptive fields. Thus, a neuron i has an
associated CPDF 
defined
over some bounded range 
of external phenomena. In
particular, the firing of neuron i represents phenomenon 
with conditional probability 
.
Clearly, such a CPDF is a field, and
so we can say that each neuron has an associated
conditional probability field.
The conditional probability field associated with a population of neurons
can then be defined in terms of field operations on the
fields of the constituent neurons.
For example, Sanger shows that over small time intervals
(such that spiking is relatively unlikely), the field of the
population is a product of the fields of the neurons that
spike in that interval:
[ _pop
= _i spike _i ,
]
where 
represents a pointwise product of the fields,
.
Further, Sanger shows that for any smooth mapping y=f(x),
there is a corresponding piecewise linear mapping on
the probability fields 
and 
, which is given by an
integral operator,
.